Probability Calculator
The Probability Calculator calculates exact, real-time domain outputs in active voice. The Probability Calculator computes event probabilities P(A ∩ B), P(A ∪ B), P(A'), P(B'), and exact Binomial distribution probabilities for k successes in n Bernoulli trials.
Interactive Probability Calculator Workspace
Launch Interactive Probability Calculator →
Probability Calculator Input Parameters & Defaults
| Probability of Event A [0 to 1] | 0.4 | Probability P(A) between 0 and 1. |
| Probability of Event B [0 to 1] | 0.5 | Probability P(B) between 0 and 1. |
| Binomial Trials (n) | 10 | Number of trials for P(A) binomial distribution. |
| Target Successes (k) | 4 | Exact number of successes k out of n trials. |
Probability Calculator Mathematical Formula
P(A \cup B) = P(A) + P(B) - P(A)P(B), \quad P(X=k) = \binom{n}{k} p^k (1-p)^{n-k}Probability Calculator Worked Example
Two independent events with P(A) = 0.40 and P(B) = 0.50.
- Both occur P(A ∩ B) = 0.40 × 0.50 = 0.20 (20%).
- At least one occurs P(A ∪ B) = 0.40 + 0.50 - 0.20 = 0.70 (70%).
- Neither occurs P(A' ∩ B') = (1 - 0.40) × (1 - 0.50) = 0.30 (30%).
Adding probabilities without subtracting their overlap P(A ∩ B) double-counts joint occurrences.
Probability Calculator Glossary of Key Terms
Probability of Event A [0 to 1] (Probability Calculator)
Probability P(A) between 0 and 1.
Probability of Event B [0 to 1] (Probability Calculator)
Probability P(B) between 0 and 1.
Binomial Trials (n) (Probability Calculator)
Number of trials for P(A) binomial distribution.
Target Successes (k) (Probability Calculator)
Exact number of successes k out of n trials.
Abstract Syntax Tree (AST)
A hierarchical tree representation of a mathematical expression that enforces operator precedence without dynamic code execution.
IEEE 754 Precision Normalization
A numerical rounding method that eliminates binary floating-point representation drift in decimal arithmetic.
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Probability Calculator Frequently Asked Questions
Q: What is the Gambler's Fallacy?
The Gambler's Fallacy is the mistaken belief that if an independent event (like a fair coin landing heads) happens repeatedly, the opposite outcome becomes 'due' on the next trial. In independent trials, memoryless probabilities remain constant.